EDB — 18J

Exercises

1. [18J]Let $f:(a,b)\to ℝ$ be convex. Show that, for every closed interval $I\subset (a,b)$, there exists a constant $C$ such that $f{|}_I$ is Lipschitz with constant $C$. Provide an example of a continuous and convex function defined on a closed interval that is not Lipschitz.